Finite Group Databasebeta

← #14782684

Subgroups — #14782684

Order 2816.

914 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077133C211yesmaximal, characteristic
2C2×#10622579C211yesmaximal, characteristic
3#13077060C211yesmaximal, characteristic
4#13070062C214yesmaximal, complemented
5#13070057C214yesmaximal, complemented
6#13068355C211yesmaximal, characteristic, complemented
7C2×#10622168C211yesmaximal, characteristic, complemented
8#13068343C211yesmaximal, characteristic, complemented
9C2×C11×#428C211yesmaximal, characteristic, complemented
10C22×#4339C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17C11×#428—22no—
18C11×#428—22no—
19C2×C11×#107C2212yescomplemented
20C2×C11×#106C2212yescomplemented
21#10622742—22no—
22#10622739—22no—
23#10622723C2214yes—
24#10622617—21no—
25#10622615—22no—
26#10622614—21no—
27C2×#66874—21no—
28#10622579—22no—
29#10622579C2214yes—
30#10622579C2212yes—
31#10622579C2212yes—
32C2×#66873—21no—
33#10622190C2214yescomplemented
34#10622168C2214yescomplemented
35#10622168C2212yescomplemented
36#10622168C2212yescomplemented
37C23×C4×C11—21no—
38C23×C4×C11C2311yescharacteristic
39C22×C22⋊D11—21no—
40C2×#4339—21no—
41C2×#4339—21no—
42C2×#4339—22no—
43C2×#4339—22no—
44C2×#4339—22no—
45C2×#4339—22no—
46C2×#4339D412yes—
47C2×#4339C2312yes—
48C22×D44D411yescharacteristic
49C22×C4×D11—21no—
50C22×Dic22D411yescharacteristic
51C2×C11×M16—22no—
52C2×C11×M16—22no—
53C2×C11×M16D412yes—
54C2×C11×M16D412yes—
55C22×C8×C11C2312yes—
56C11×#117—21no—
57C11×#117—21no—
58C11×#117—21no—
59C11×#117—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C22⋊C4—21no—
69C2×C42×C11—21no—
70C2×#4318—21no—
71C2×#4318—21no—
72C2×#4318—21no—
73C2×#4318—22no—
74C2×#4318—22no—
75C2×#4318—22no—
76C2×#4318—22no—
77C2×#4318—22no—
78C2×#4318—22no—
79C2×#4318C2312yes—
80C2×#4318C2312yes—
81C2×#4318C2312yes—
82C22×C11⋊C8—21no—
83C22×C11⋊C8—21no—
84C22×C11⋊C8—21no—
85C11×#107—24no—
86C11×#106—24no—
87(C2×D11)⋊C8—28no—
88#66874—24no—
89#66874—22no—
90#66874—22no—
91#66873—24no—
92#66873—22no—
93#66873—22no—
94#23647—111nomaximal, Sylow
95C24×C11#4111yescharacteristic
96C23×D11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—82no—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11#4111yescharacteristic
108C22×C4×C11#4112yes—
109C22×C4×C11#4112yes—
110C22×C4×C11#4112yes—
111C22×C4×C11#4112yes—
112C22×C4×C11C2411yescharacteristic
113C2×C22⋊D11—22no—
114C2×C22⋊D11—22no—
115C2×C22⋊D11—42no—
116C2×C22⋊D11—42no—
117C22×Dic11—21no—
118#4339—24no—
119#4339—24no—
120#4339—22no—
121#4339—22no—
122#4339—22no—
123#4339—22no—
124#4339—42no—
125#4339—42no—
126#4339—42no—
127#4339—42no—
128C2×D44—21no—
129C2×D44—22no—
130C2×D44—22no—
131C2×D44C2×D412yes—
132C2×C4×D11—22no—
133C2×C4×D11—22no—
134C2×C4×D11—42no—
135C2×C4×D11—42no—
136C2×Dic22—21no—
137C2×Dic22—22no—
138C2×Dic22—22no—
139C2×Dic22C2×D412yes—
140C11×M16—24no—
141C11×M16—24no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C2×C8×C11C2×D414yes—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—41no—
152C11×C4⋊C4—41no—
153C11×C22⋊C4—41no—
154C11×C22⋊C4—41no—
155C42×C11—41no—
156C42×C11—41no—
157#4318—22no—
158#4318—22no—
159#4318—22no—
160#4318—22no—
161#4318—22no—
162#4318—22no—
163#4318—42no—
164#4318—42no—
165#4318—42no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—42no—
170C2×C11⋊C8—42no—
171C2×C11⋊C8—42no—
172C2×#428D1111yescharacteristic, complemented
173#2896—111no—
174C2×#417—111no—
175#2879—111no—
176#2079—114no—
177#2078—114no—
178#1742—111no—
179C2×#343—111no—
180#1738—111no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11#12111yescharacteristic
184C23×C11#12111yescharacteristic
185C23×C11#12612yes—
186C23×C11#12612yes—
187C23×C11C2×#4111yescharacteristic
188C22×D11—22no—
189C22×D11—42no—
190C22×D11—81no—
191C22×D11—81no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—42no—
195C2×C4×C11—82no—
196C2×C4×C11—82no—
197C2×C4×C11—81no—
198C2×C4×C11—81no—
199C2×C4×C11—82no—
200C2×C4×C11#12111yescharacteristic
201C2×C4×C11#12111yescharacteristic
202C2×C4×C11#12312yes—
203C2×C4×C11#12312yes—
204C2×C4×C11#12312yes—
205C2×C4×C11#12312yes—
206C2×C4×C11#12312yes—
207C2×C4×C11#12312yes—
208C2×C4×C11#12412yes—
209C2×C4×C11#12412yes—
210C2×C4×C11#12612yes—
211C2×C4×C11#12612yes—
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11C2×#4111yescharacteristic
218C22⋊D11—42no—
219C22⋊D11—42no—
220C22⋊D11—44no—
221C2×Dic11—22no—
222C2×Dic11—42no—
223D44—22no—
224D44—22no—
225D44—42no—
226C4×D11—42no—
227C4×D11—42no—
228C4×D11—44no—
229Dic22—22no—
230Dic22—22no—
231Dic22—42no—
232C8×C11—24no—
233C11⋊C8—42no—
234C11⋊C8—42no—
235C11⋊C8—42no—
236C22×#41—111no—
237C22×M16—111no—
238C22×M16—111no—
239C22×M16—111no—
240C22×M16C2×D1111yescharacteristic
241C2×#117C2×D1111yescharacteristic
242C22×C4⋊C4C2×D1111yescharacteristic
243#428—22no—
244#428—22no—
245C2×#107C2×D1112yescomplemented
246C2×#106C2×D1112yescomplemented
247#419—221no—
248#418—221no—
249#417—112no—
250#417—114no—
251#417—112no—
252#417—222no—
253#416—222no—
254C2×#103—221no—
255C2×#102—221no—
256#408—114no—
257#408—222no—
258#407—222no—
259#343—112no—
260#343—114no—
261#343—112no—
262#341—114no—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11#39712yes—
272C22×C11#39712yes—
273C22×C11C2×#12111yescharacteristic
274C22×C11C2×#12611yescharacteristic
275C22×C11C2×#12611yescharacteristic
276C2×D11—42no—
277C2×D11—42no—
278C2×D11—42no—
279C2×D11—84no—
280C4×C11—81no—
281C4×C11—82no—
282C4×C11—81no—
283C4×C11#39712yes—
284C4×C11#39712yes—
285C4×C11C2×#12311yescharacteristic
286C4×C11C2×#12311yescharacteristic
287C4×C11C2×#12311yescharacteristic
288C4×C11C2×#12411yescharacteristic
289Dic11—42no—
290C2×#41—112no—
291C2×#41—112no—
292C2×#41—221no—
293C2×#41—221no—
294C2×#41—222no—
295C2×#41—222no—
296C2×#41—222no—
297C2×#41—222no—
298C22×Q8—111no—
299C22×D4—111no—
300C22×D4—221no—
301C23×C4—21no—
302C23×C4—221no—
303C23×C4C22×D1111yescharacteristic
304C2×M16—22no—
305C2×M16—22no—
306C2×M16—112no—
307C2×M16—112no—
308C2×M16—112no—
309C2×M16—221no—
310C2×M16—221no—
311C2×M16—221no—
312C2×M16—222no—
313C2×M16—222no—
314C2×M16—222no—
315C2×M16—222no—
316C2×M16—222no—
317C2×M16—222no—
318C2×M16C22⋊D1112yes—
319C2×M16C22⋊D1112yes—
320C22×C8—221no—
321C22×C8—221no—
322C22×C8—221no—
323C22×C8C22×D1112yes—
324#117—21no—
325#117—21no—
326#117—21no—
327#117—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4C22×D1112yes—
334C2×C4⋊C4C22×D1111yescharacteristic
335C2×C4⋊C4C22×D1111yescharacteristic
336C2×C22⋊C4—21no—
337C2×C42—21no—
338#107—24no—
339#106—24no—
340#103—224no—
341#103—222no—
342#103—222no—
343#102—224no—
344#102—222no—
345#102—222no—
346C22⋊C8—228no—
347C2×C11—22no—
348C2×C11—21no—
349C2×C11—21no—
350C2×C11—22no—
351C2×C11C2×#39711yescharacteristic
352C2×C11#306811yescharacteristic
353C2×C11#306911yescharacteristic
354D11—82no—
355C24—221no—
356C24#434111yescharacteristic
357#41—224no—
358#41—224no—
359#41—222no—
360#41—222no—
361#41—222no—
362#41—222no—
363#41—442no—
364#41—442no—
365#41—442no—
366#41—442no—
367C2×Q8—112no—
368C2×Q8—221no—
369C2×Q8—222no—
370C2×Q8—222no—
371C2×D4—112no—
372C2×D4—222no—
373C2×D4—222no—
374C2×D4—222no—
375C2×D4—222no—
376C2×D4—221no—
377C2×D4—442no—
378C2×D4—442no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—82no—
385C22×C4—221no—
386C22×C4—222no—
387C22×C4—222no—
388C22×C4—442no—
389C22×C4—442no—
390C22×C4#433912yes—
391C22×C4#433912yes—
392C22×C4D4×D1111yescharacteristic
393C22×C4D4×D1111yescharacteristic
394C22×C4#434111yescharacteristic
395C22×C4#434312yes—
396C22×C4#434312yes—
397C22×C4C2×C22⋊D1111yescharacteristic
398C22×C4C2×C22⋊D1111yescharacteristic
399C22×C4C23×D1111yescharacteristic
400M16—24no—
401M16—24no—
402M16—222no—
403M16—222no—
404M16—222no—
405M16—222no—
406M16—222no—
407M16—222no—
408M16—442no—
409M16—442no—
410M16—442no—
411C2×C8—22no—
412C2×C8—22no—
413C2×C8—222no—
414C2×C8—222no—
415C2×C8—222no—
416C2×C8—442no—
417C2×C8—442no—
418C2×C8—442no—
419C2×C8C2×C22⋊D1114yes—
420C4⋊C4—22no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—22no—
425C4⋊C4—21no—
426C4⋊C4—41no—
427C4⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C42—41no—
431C42—41no—
432C11#2364711yescharacteristic, complemented, Sylow
433C23—41no—
434C23—41no—
435C23—222no—
436C23—442no—
437C23—881no—
438C23—881no—
439C23#6695112yes—
440C23#6695112yes—
441C23#6699111yescharacteristic
442C23#6699111yescharacteristic
443C23C2×#434111yescharacteristic
444Q8—222no—
445Q8—222no—
446Q8—442no—
447D4—222no—
448D4—222no—
449D4—442no—
450D4—442no—
451D4—444no—
452D4—442no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—82no—
457C2×C4—82no—
458C2×C4—81no—
459C2×C4—81no—
460C2×C4—82no—
461C2×C4—222no—
462C2×C4—442no—
463C2×C4—442no—
464C2×C4—442no—
465C2×C4—444no—
466C2×C4#6694712yes—
467C2×C4#6694712yes—
468C2×C4#6694712yes—
469C2×C4#6694712yes—
470C2×C4#6695112yes—
471C2×C4#6695112yes—
472C2×C4#6698212yes—
473C2×C4#6698212yes—
474C2×C4#6699111yescharacteristic
475C2×C4#6699111yescharacteristic
476C2×C4#6700012yes—
477C2×C4#6700012yes—
478C2×C4C2×#433911yescharacteristic
479C2×C4C2×#433911yescharacteristic
480C2×C4C2×D4×D1111yescharacteristic
481C2×C4C2×#434311yescharacteristic
482C2×C4C2×#434311yescharacteristic
483C2×C4C22×C22⋊D1111yescharacteristic
484C8—24no—
485C8—442no—
486C8—442no—
487C8—442no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—42no—
495C22—42no—
496C22—442no—
497C22—442no—
498C22—442no—
499C22—884no—
500C22#1062260612yes—
501C22#1062260612yes—
502C22C2×#6695111yescharacteristic
503C22C2×#6695111yescharacteristic
504C22C2×#6699111yescharacteristic
505C4—82no—
506C4—81no—
507C4—81no—
508C4—442no—
509C4#1062260612yes—
510C4#1062260612yes—
511C4C2×#6694711yescharacteristic
512C4C2×#6694711yescharacteristic
513C4C2×#6698211yescharacteristic
514C4C2×#6700011yescharacteristic
515C2—22no—
516C2—21no—
517C2—21no—
518C2—22no—
519C2—882no—
520C2C2×#1062260611yescharacteristic
521C2#1307834011yescharacteristic
522C2#1307834911yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#428C2
socleC22×C11C2×#121
prime radicalC22×#4339C22
hypercenterC2×#428D11
hypocenterC11#23647
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#428

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #13070062C2semidirect
5. #13070057C2semidirect
6. #13068355C2semidirect
7. C2×#10622168C2semidirect
8. #13068343C2semidirect
9. C2×C11×#428C2semidirect
19. C2×C11×#107C22semidirect
20. C2×C11×#106C22semidirect
33. #10622190C22semidirect
34. #10622168C22semidirect
35. #10622168C22semidirect
36. #10622168C22semidirect
172. C2×#428D11semidirect
245. C2×#107C2×D11semidirect
246. C2×#106C2×D11semidirect
432. C11#23647semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130771332
C2×#106225792
#130770602
#130700622
#130700572
#130683552
C2×#106221682
#130683432
C2×C11×#4282
#2364711